Non-commutative integrable systems on $b$-symplectic manifolds

Abstract

In this paper we study non-commutative integrable systems on $b$-Poisson manifolds. One important source of examples (and motivation) of such systems comes from considering non-commutative systems on manifolds with boundary having the right asymptotics on the boundary. In this paper we describe this and other examples and we prove an action-angle theorem for non-commutative integrable systems on a $b$-symplectic manifold in a neighbourhood of a Liouville torus inside the critical set of the Poisson structure associated to the $b$-symplectic structure.

References in corpus (4)

• Examples of integrable and non-integrable systems on singular symplectic manifolds
• Cotangent models for integrable systems
• Action-angle variables and a KAM theorem for b-Poisson manifolds
• Weakly Hamiltonian actions

Cited by in corpus (6)

• Reduction theory for singular symplectic manifolds and singular forms on moduli spaces
• Integrable systems in cosymplectic geometry
• A $b$-symplectic slice theorem
• Contact line bundles, foliations, and integrability
• E-structures and almost regular Poisson manifolds
• Integrable systems on singular symplectic manifolds: From local to global